The generator matrix

 1  0  1  1  1  1  1  1  1  0
 0  1 X+1 X^2+X X^2+1 X^3+X^2 X^3+X^2+X+1 X^3+X X^2+1  X
 0  0 X^3  0  0  0 X^3 X^3 X^3 X^3
 0  0  0 X^3  0 X^3 X^3 X^3  0 X^3
 0  0  0  0 X^3 X^3  0 X^3 X^3  0

generates a code of length 10 over Z2[X]/(X^4) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+20x^7+162x^8+480x^9+704x^10+520x^11+152x^12+4x^15+5x^16

The gray image is a linear code over GF(2) with n=80, k=11 and d=28.
This code was found by Heurico 1.16 in 0.141 seconds.